One of the most common answers to this question is that from the past we can understand more about the present. Only by drawing on how a language has changed over time, we can understand why this language has its current grammatical structures or phonological rules.
However, this is not the only reasons why Historical Linguistics is interesting. It allows Linguists to compare different methodologies which have been used in the past and to evaluate which ones provide us with more information and are the most efficient. Historical Linguistics also allows Linguists to explore languages which do not exist anymore, such as Gothic, Old English, Latin, Sanskrit and so on.
It is fascinating to attempt to reconstruct how these languages might have sounded, and how they would have been written and used. Moreover, studying Historical Linguistics allows Linguists to inevitably learn more about the culture, customs, religion and literature of the language studied in question and to gain a diachronic perspective of such aspects. This is crucial as Languages have been greatly influenced by the culture of their speakers.
Finally, the fact that the field of Historical Linguistics exists is a sign that Linguistics is gradually becoming a very important subject – one which is worthy of attention.
As Robins affirms (1967: v), “the current interest shown by linguists in the past developments and the earlier history of their subject is in itself a sign of the maturity of linguistics as an academic discipline, quite apart from any practical applications of linguistic science”.
Robins, R. H. (1967) A Short History of Linguistics. London: Longman.